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Unit IV: Work, Energy, & Momentum Guided Notes
Name:_____________________
What is work?
Work W is done when a constant force F exerted on an object through distance d
W = Fdd = Fd cosθ
 Only the component of force that acts in the __________________________________________ is doing work
on the box.
 The SI unit for work is the newton–metre and is called the joule named after the 19th Century physicist James
Prescott Joule.
 1 J (Joule) = 1N x 1 m
 Work is a scalar (add like ordinary numbers)
Is it work?
To be work, something must MOVE.
 you are NOT doing work if you are just holding a weight above your head (no distance moved)
 you do work only while you are lifting the weight above your head (force in the direction of distance moved)
To be work, at least a component of the force must be in the plane of the movement
 If the force and the movement are at a 90o angle, then there is NO work (example, holding something and
carrying it across a room)
 If the force and the movement are generally in the same direction, then there is positive work (example, pushing
a box across the room)
 If the force and the movement are generally in the opposite direction, then there is negative work (example,
friction).
We Do
1) Is work positive, negative, or zero?
a) a book falls off a table
b) a rocket accelerates through space
2) Mike is cutting the grass using a human-powered lawn mower. He pushes the mower with a force of 45 N
directed at an angle of 41° below the horizontal direction. Calculate the work that Mike does on the mower in
pushing it 9.1 m across the yard
You Do
1) Is work positive, negative, or zero?
a) A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed.
b) friction slows a sliding hockey puck
2) Forward force is 200 N. Friction force is 200 N. The distance moved is 200 km. Find
a) the work done by forward force F on the car.
b) the work done by friction force Ffr on the car.
c) the net work done on the car.
Determining work from a graph of Force vs Distance
In general: The area under a Force - distance graph equals the work done by that force
 The lady from the first slide is pulling the car for 2 m with force of 160 N at the angle of 60o , then she gets tired
and lowers her arms behind her at an angle of 45o pulling it now with 170 N for next 2 m. Finally seeing the end
of the journey she pulls it horizontally with the force of 40 N for 1 m.
 Work done by her on the car is:
W = (160 N)(cos 60o)(2m) +(170 N)(cos 45o)(2m) + (40 N)(cos 0o)(1m)
W = 80x2 + 120x2 + 40x1 = pink area + green area + blue area = 440 J
Determining work from a graph of Force vs Distance – You Do
A man pushes a cart 6m. What is the
work done?
Power
Power is the _________________________________ or energy converted in unit time.
P=
W
t
or P =
E
t
Power measures how _________________________ or how quickly energy is converted.
Units: 1 Watt (W) = 1 Joule (J) / s
example: A 100 W light bulb converts electrical energy to heat and light at the rate of 100 J every second.
Power - We do
Calculate the power of a worker in a supermarket who stacks shelves 1.5 m high with cartons of orange juice, each of
mass 6.0 kg, at the rate of 30 cartons per minute.
Efficiency
Efficiency is the ratio of how much work, energy or power we get out of a system compared to how much is put in.
efficiency =
useful output
total input
eff =
Wout
E
P
= out = out
Win
Ein
Pin
No units
Efficiency can be expressed as percentage by multiplying by 100%.
No real machine can ever be 100% efficient, because there will always be some energy lost as heat
Efficiency – We do
A car engine has an efficiency of 20 % and produces an average of 25 kJ of useful work per second.
How much energy is converted into heat per second?
Power and Efficiency You Do
 An elevator lifts a total mass of 1.1X103 kg a distance of 40.0 m in 12.5 s. How much power does the
elevator deliver?
 What work is required to lift a 215 kg mass a distance of 5.65 m, using a machine that is 72.5%
efficient?
Energy
Energy = ____________________________
And, in reverse…
work done = change in energy
Work-energy
theorem
Units: ______________________
W=∆E
Two major types of energy
1) ____________________________ –
energy that is ______________ due to an object’s position.
Examples:
gravitational potential energy
elastic potential energy
2) ____________________________ -
energy of _______________
Gravitational Potential Energy
Stored energy due to an ___________________. The higher the object, the more gravitational potential energy.**
PEg = mgh
Elastic Potential Energy
Energy stored due the _____________________________________________ of elastic material, such as a spring.
Fspring = kx (Hooke’s Law)
where k is the spring constant and x is the distance the spring has been stretched or compressed.
Pespring = ½ kx2
Potential Energy and Work
We said earlier that W = Δ E
and we know that potential energy depends only on the position of an object…
THIS IMPLIES THAT WHEN DOING WORK, THE PATH DOESN’T MATTER --- ONLY THE END POSITION
Work depends on _______________________________________ NOT on __________________
Work equals _____________________________________________________.
Ramps
How does a ramp make moving objects easier?
Ramps can’t reduce the work, but they can reduce the force necessary. To move an object up a certain height, we can
either exert a lot of force over a short distance (lifting it), or we can exert a smaller force over a larger distance (pushing
up a ramp).
PE and Work – You Do
a) A cart filled with bricks is
pulled at constant speed up
a ramp. The cart has a
mass of 3.0kg and the height
of the ramp is 0.45 m.
What is the PEg of the cart at
the top of the ramp?
b) It required 14.7 N to pull the cart up the ramp, and the ramp is 0.9 m long. How much work was needed to pull the
cart up the ramp?
Kinetic Energy
Kinetic energy is the energy of ___________________________.
KE = ½ m v2
where v = velocity
This means that a moving object possesses the ________________________________________.
Example: A hammer by virtue of its motion can be used to do work in driving a nail into a piece of wood
We Do – Kinetic Energy
(1) A father pushes his child on a sled on level ice, a distance 5 m from rest, giving a final speed of 2 m/s. If the
mass of the child and sled is 30 kg, how much work did he do?
(2) What is the average force he exerted on the child?
(3) A 1000-kg car going at 45 km/h. When the driver slams on the brakes, the road does work on the car through a
backward-directed friction force.
How much work must this friction force do in order to stop the car?
(4) Instead of slamming on the brakes the work required to stop the car is provided by a tree!!!
What average force is required to stop a 1000-kg car going at 45 km/h if the car collapses one foot (0.3 m) upon
impact?
You Do – Kinetic Energy
 Determine the KE of a 625 kg roller coaster that is moving with a speed of 18.3 m/s.
 What would the KE be if the roller coaster doubled its speed?
KE and Work – You Do
 Determine the KE of a 625 kg roller coaster that is moving with a speed of 18.3 m/s.
 What would the KE be if the roller coaster doubled its speed?
Conservation of Energy Guided Notes
In a closed system, energy is neither created nor destroyed. Energy simply changes from one form to another.
____________________________________________________
 Mostly, we will use this in situations without friction to say:
_________________________________________________
 We can also use this in situations where energy is converted to heat due to friction or air resistance to say:
________________________________________________
Conservation of energy is a very useful tool to solve physics problems!
Many problems that can be solved using Newton’s laws can be solved much easier by applying conservation of energy.
Example: Find the final velocity of a block that is released from rest at the top of a ramp.
Method One: Newton’s Law
Method Two: Conservation of Energy
Examples of Conservation of Energy: Free Fall
Free fall in the absence of air resistance
A 10 kg ball is dropped from a height of 102 m. What is its velocity when it hits the ground?
Free fall when air resistance is significant
A 10 kg ball is dropped from a height of 102 m. When it hits the ground, it has a final velocity of 40m/s. How much
energy was ‘lost’ due to air resistance?
You Do: Water Slide
A child of mass m is released from rest at the top of a water slide, at height h = 8.5 m above the bottom of the slide.
Assuming that the slide is frictionless because of the water on it, find the child’s speed at the bottom of the slide.
Check your understanding: Roller coaster tracks
Assuming that the track is frictionless, at what point(s) is
the total energy of the system the same as in point A ?
1.
2.
3.
4.
5.
B
C
D
All of the above
none of the above
Assuming the track is frictionless, at what height will the ball end up?
1.
2.
3.
4.
same height as A
lower height than A
higher height than A
impossible to determine
If the track does have friction, at what height will the ball end up?
1. same height as A
2. lower height than A
3. higher height than A
4. impossible to determine
At what point(s) does the ball have a combination of PE and KE?
1. A
2. B
3. C
4. D
5. B and C
Check your understanding – projectile motion
Three balls are thrown from the top of the cliff along paths A, B, and C with the same initial speed (air resistance is
negligible). Which ball strikes the ground below with the greatest speed?
1. A
2. B
3. C
4. All strike with the same speed
Check your understanding – pendulum
A pendulum swings back and forth. At which point or points along the pendulum’s path …
1) Is PE greatest?
2) Is KE greatest?Is speed greatest?
An ideal pendulum would keep going forever.
Why do real pendulums eventually stop?
We do – roller coaster tracks
A car (toy car – no engine) is at the top of a hill on a frictionless track. What must the car’s speed be at the top of the
first hill if it can just make it to the top of the second hill?
You do – simple pendulum
A simple pendulum consists of a 2.0 kg mass attached to a string. It is released from rest at A as shown. Its speed at the
lowest point B is:
You Do – block sliding down a ramp with and without friction
Linear Impulse and Momentum Guided Notes
Momentum (p)
Momentum is mass times velocity
momentum is a ____________________________!
momentum has units _____________________
Which has more momentum?
 1 kg object moving at 1000 m/s -or- a 1000 kg object moving at 1 m/s?
 a rolling marble –or-stationary truck?
 a marble moving at 0.5 m/s –or- truck moving at 0.5 m/s?
The way we use the word ‘momentum’ in everyday life actually does relate to its physics definition.
For example, in game, a sports announcer might say that one team ‘has momentum’. What do they mean?
The sports announcer means that the team ______________________________________ and is going to be
______________________________.
In this way, the everyday usage and the physics definition of momentum are the same:
________________________________________________________________________________________________
How do we change momentum?
Since mass doesn’t (usually) change, a change in momentum occurs when the _______________________ of an object
changes.
What is necessary to change an object’s velocity? ____________________________________
Changes in momentum are produced by the action of _______________________________________.
Force applied over time _________________________ is an called an________________________.
Impulse & Momentum
Is it harder to stop an object with more mass or less?
Is it harder to stop a fast moving object or a slow moving object?
Two cars are moving with the same velocity. In car A, the driver applies the brakes, and the car stops due to the force
of friction. The time period over which friction acts is 30 seconds. Car B hits a tree. The time period over which the
tree applies a force is 0.5 seconds.
How does the change in momentum of the two objects compare?
How does the force applied in each circumstance compare?
Other examples of minimizing force applied by maximizing time of contact
We do
You do
1) A compact car with mass 725 kg is moving 115 km/hr to the East. The driver suddenly applies the brakes hard
for 2.0s, applying an average force of 5.0 X 103 N on the car.
a) What is the change in momentum of the car?
b) What is the final velocity of the car?
2. In a ballistics test at the police department, Officer Rios fires a 6.0 g bullet at 350 m/s into a container that stops
it in 0.0018 s. What is the average force that stops the bullet?
Graphical Determination of Momentum
In the problems we’ve done so far, the we’ve dealt with average or constant force. If force changes over time, we can
find the change in momentum graphically.
Change in momentum, Δp, is the _______________________________________________________________.
The graph shows the force applied to a 57 g
tennis ball by a racquet over time.
a) What is the change in momentum?
b) If the ball starts at rest, what is
its final velocity?
You Do
a) What is the change in momentum of
the football as a result of being
kicked?
b) If the football started at rest, what is
its final velocity? (mass = 400 g)
Conservation of Momentum
● In any closed system (no external force) total momentum is conserved.
● When we have more than one object,
OR
Example: Explosion / Ejection
A 60.0-kg astronaut is on a space walk when her tether line breaks. She throws her 10.0-kg oxygen tank away
from the shuttle with a speed of 12.0 m/s to propel herself back to the shuttle. What is her velocity?
We Do Collision Problem
There are two fish in the sea. A 6 kg fish and a 2 kg fish. The big fish swallows the small one. What is its
velocity immediately after lunch?
a. the big fish swims at 1 m/s toward and swallows the small fish that is at rest.
b. Suppose the small fish is not at rest but is swimming toward the large fish at 2 m/s.
c. Small fish swims toward the large fish at 3 m/s.
d. Small fish swims toward the large fish at 4 m/s.
What if the objects travel at angles to each other???
 Resolve vectors into components
 Apply conservation of momentum to the x direction and the y direction.
-
AND -
Example 1
A red ball traveling with a speed of 2 m/s along the x-axis hits the eight ball. After the collision, the red ball
travels with a speed of 1.6 m/s in a direction 37o below the positive x-axis. The two balls have equal mass. At
what angle will the eight ball fall in the side pocket? What is the speed of the blue (8 th) ball after collision.
Example 2
Example 3
Example 4